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Let $F=\mathbb{C}((t))$. Let $G=GL_n$. Then $G(F)$ acts on $\mathfrak{g}(F)$ by gauge transformation: $$ g.x:=gxg^{-1} + \dot{g}g^{-1},\quad \quad g\in G(F), \quad x\in \mathfrak{g}(F). $$ Here, $\...

I just started reading "On the functional equations satisfied by Eisentstein series" by Langlands http://publications.ias.edu/sites/default/files/Eisenstein-ps.pdf . I wasn't sure of some notation/...